Question

Two discs have the same mass and thickness. Their materials are of densities ${\rho }_1$ and ${\rho }_2$. The ratio of their moment of inertia about a central axis will be

• A. $1:{\rho }_1{\rho }_2$
• B. ${\rho }_2:{\rho }_1$
• C. ${\rho }_1:{\rho }_2$
• D. ${\rho }_1{\rho }_2:1$

Answer 1

The correct option is B ${\rho }_2:{\rho }_1$

Moi of circular disc = $\frac{m{r}^2}{2}$

volume of disc 1 =$\frac{mass}{density}=\frac{m}{{\rho }_1}$

= $A\times t=\pi r_1^2\times b$

volume of disc 2 =$\frac{m}{{\rho }_2}$

=$A\times t=\pi r_2^2\times b$

Ratio of moi

$\frac{I_1}{I_2}=\frac{\frac{1}{2}m\times r_1^2}{\frac{1}{2}m\times r_2^2}$

= $\frac{{\rho }_2}{{\rho }_1}$